On Wed, 31 Jan 2007, Vegard Nossum wrote:
> On Tue, January 30, 2007 3:12 pm, Jan Engelhardt wrote:
> >
> >>> Why the qualifier? Zero *is* not a power of 2, is it?
> >
> > No, it is not:
> >
> > In[1]:= Solve[2^n == 0, n]
> >
> > Out[1]= {}
> >
> > So says Mathematica5.
>
> As a side note, I would just like to point out that Mathematica does
> not deal with modular arithmetic by default (which programmers very
> much do). In fact, in modular arithmetic, zero IS a power of two.
>
> 2^n = 0 (mod 2^n)
>
> To see if it holds for bytes, substitute n = 8, and you get 2^8 = 0
> (mod 256). In other words: Zero is the eighth power of two modulo
> 256.
that's a bit esoteric but, yes, you make a good point.
> Modular arithmetic is, however, very often a source of errors in
> programming (unchecked-for overflows and underflows), and it is
> questionable whether the programmer would really want 0 reported as
> a power of two.
precisely. given the definition of "is_power_of_2()" that's been
published, some people will (quite correctly) point out that using
that macro in place of the test "(n & (n - 1))" isn't quite the same
thing. and they would be correct.
but one wonders how many programmers have been using that very test
"((n & (n - 1))" without realizing that it would accept zero, and that
it has been accepting zero all this time, perhaps leading to weird and
inexplicable errors.
rewriting that test as "is_power_of_2()" may, in fact, cause some
things to suddenly break, but perhaps those are things that should
have been *forced* to break anyway, to identify where the condition
check was incorrect all this time, and someone's just been lucky, or
something like that.
***NOTE***: and that's why i suggested that the individual
maintainers might want to make this substitution themselves, to make
sure everything continues to work. because if you leave it as a
project for the kernel janitors, they might not realize what you had
in mind. so it's in your best interest to start cleaning this up on
your own.
just my $0.02 (Cdn.)
rday
--
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Robert P. J. Day
Linux Consulting, Training and Annoying Kernel Pedantry
Waterloo, Ontario, CANADA
http://www.fsdev.dreamhosters.com/wiki/index.php?title=Main_Page
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